What is it about?
Brittle materials such as glass and glass ceramics can breake when two conditions coincide. There is tensile stress acting at the surface and there are micro cracks present at the same location. Specimens ground with bonded diamonds or lapped with silicon carbide grains prepared in a well-defined way and loaded with linearly rising stress will break at different stress values. Breakage will start from the deepest micro crack among many thousands, which are present in the surface. It is expected that the breakage values will follow a statistical distribution which relates to the probability for the deepest micro cracks, the extreme values of the statistical depth distribution of all micro cracks. This is the Weibull distribution. Traditionally, it has been used in itw two parameter version without the location parameter. The paper demonstrates that this approach is not supported by experiment. This proof needs larger samples than used in the past. The threshold breakage stress can be seen only with samples of more than about 100 specimens. Calculations of lifetimes of brittel items on the basis of the two parameter Weibull distributions are misleading and contradictory. They lead to allowable stresses much lower than in reality and predict earlier breakage for surface conditions, which have proven in practice to be much stronger. The presented data clearly prove the existence of a threshold breakage stress, which corresponds with the existence of a maximum micro crack depth in the surfaces. Together with the well established crack growth law and fatigue mechanism this allows calculating minimum lifetime before any breakage will occur.
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Why is it important?
The two parameter approach states a purely statistical behavior of glass items' breakage under tensile loads. This paper demonstrates that there is a threshold stress. Below it there is a deterministic range, where no breakage will occur at all. This allows applying glass items at higher loads with improved reliability.
Perspectives
This is a paper in a series of publications on the subject deterministic approach for glass lifetime calculation. It is of wide applicability to technical glass far beyond glass ceramics and optical glasses. The general results hold for any glass objects with well defined surfaces and can serve as a guideline for surfaces with less good definition. It points out that with some higher effort for producing and measuring larger samples one can obtain very valuable knowledge about the breakage behavior being worth far more than the investment. Higher allowable loads with higher reliability might open new application possibilities for glass. I see it as a revolution in the strength of glass and glass ceramics.
Dr Peter Hartmann
SCHOTT AG retired
Read the Original
This page is a summary of: ZERODUR strength modeling with Weibull statistical distributions, July 2016, SPIE,
DOI: 10.1117/12.2231608.
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